论文标题
部分饱和土壤的热力学处理\\揭示了有效应力的结构
A Thermodynamic Treatment\\ of Partially Saturated Soils \\ Revealing the Structure of Effective Stress
论文作者
论文摘要
储层计算是预测湍流的有力工具,其简单的架构具有处理大型系统的计算效率。然而,其实现通常需要完整的状态向量测量和系统非线性知识。我们使用非线性投影函数将系统测量扩展到高维空间,然后将其输入到储层中以获得预测。我们展示了这种储层计算网络在时空混沌系统上的应用,该系统模拟了湍流的若干特征。我们表明,使用径向基函数作为非线性投影器,即使只有部分观测并且不知道控制方程,也能稳健地捕捉复杂的系统非线性。最后,我们表明,当测量稀疏、不完整且带有噪声,甚至控制方程变得不准确时,我们的网络仍然可以产生相当准确的预测,从而为实际湍流系统的无模型预测铺平了道路。
A rigorous thermodynamic treatment of partially saturated soils is developed using a minimal number of assumptions. The derivation is carried out in a way that does not require to explicitly track the complex shapes of interfaces between the solid, fluid and gas domains. Instead, suction is the property being recovered explicitly through the minimisation of energy around an ideal `suctionless limit', while considering the different compressibilities of the three domains. In interpreting experimental data the derivation ensures the thermodynamic equilibrium between the chemical potentials of the soil and measurement cells, while carefully distinguishing intrinsic from measured pressures and suctions. A most general expression for the effective stress of partially saturated soils is then derived that is strictly linked to the soil-water retention curve (SWRC). The structure of the effective stress broadly depends on the three thermodynamic densities characterising the solid, fluid and gas domains. Special cases of SWRC are explored, which reveals conditions for which the structure of the effective stress may agree with previously proposed empirical relationships.